Properties

Label 1441.2
Level 1441
Weight 2
Dimension 83197
Nonzero newspaces 28
Sturm bound 343200
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1441 = 11 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(343200\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1441))\).

Total New Old
Modular forms 87100 85521 1579
Cusp forms 84501 83197 1304
Eisenstein series 2599 2324 275

Trace form

\( 83197 q - 519 q^{2} - 522 q^{3} - 531 q^{4} - 528 q^{5} - 536 q^{6} - 524 q^{7} - 535 q^{8} - 529 q^{9} + O(q^{10}) \) \( 83197 q - 519 q^{2} - 522 q^{3} - 531 q^{4} - 528 q^{5} - 536 q^{6} - 524 q^{7} - 535 q^{8} - 529 q^{9} - 534 q^{10} - 588 q^{11} - 1194 q^{12} - 542 q^{13} - 552 q^{14} - 542 q^{15} - 543 q^{16} - 534 q^{17} - 567 q^{18} - 540 q^{19} - 566 q^{20} - 556 q^{21} - 584 q^{22} - 1192 q^{23} - 580 q^{24} - 543 q^{25} - 546 q^{26} - 570 q^{27} - 568 q^{28} - 550 q^{29} - 596 q^{30} - 566 q^{31} - 599 q^{32} - 587 q^{33} - 1232 q^{34} - 564 q^{35} - 603 q^{36} - 564 q^{37} - 580 q^{38} - 568 q^{39} - 610 q^{40} - 546 q^{41} - 608 q^{42} - 552 q^{43} - 596 q^{44} - 1244 q^{45} - 596 q^{46} - 584 q^{47} - 652 q^{48} - 571 q^{49} - 629 q^{50} - 596 q^{51} - 634 q^{52} - 562 q^{53} - 620 q^{54} - 593 q^{55} - 1290 q^{56} - 600 q^{57} - 610 q^{58} - 590 q^{59} - 684 q^{60} - 606 q^{61} - 588 q^{62} - 632 q^{63} - 631 q^{64} - 612 q^{65} - 601 q^{66} - 1224 q^{67} - 638 q^{68} - 618 q^{69} - 672 q^{70} - 586 q^{71} - 715 q^{72} - 602 q^{73} - 622 q^{74} - 652 q^{75} - 660 q^{76} - 589 q^{77} - 1354 q^{78} - 580 q^{79} - 698 q^{80} - 643 q^{81} - 678 q^{82} - 592 q^{83} - 752 q^{84} - 624 q^{85} - 676 q^{86} - 640 q^{87} - 600 q^{88} - 1290 q^{89} - 762 q^{90} - 616 q^{91} - 684 q^{92} - 634 q^{93} - 632 q^{94} - 640 q^{95} - 756 q^{96} - 604 q^{97} - 703 q^{98} - 594 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1441))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1441.2.a \(\chi_{1441}(1, \cdot)\) 1441.2.a.a 1 1
1441.2.a.b 1
1441.2.a.c 23
1441.2.a.d 23
1441.2.a.e 28
1441.2.a.f 31
1441.2.d \(\chi_{1441}(1440, \cdot)\) n/a 130 1
1441.2.e \(\chi_{1441}(89, \cdot)\) n/a 440 4
1441.2.f \(\chi_{1441}(394, \cdot)\) n/a 520 4
1441.2.g \(\chi_{1441}(58, \cdot)\) n/a 520 4
1441.2.h \(\chi_{1441}(53, \cdot)\) n/a 520 4
1441.2.i \(\chi_{1441}(708, \cdot)\) n/a 520 4
1441.2.j \(\chi_{1441}(192, \cdot)\) n/a 520 4
1441.2.m \(\chi_{1441}(864, \cdot)\) n/a 520 4
1441.2.n \(\chi_{1441}(340, \cdot)\) n/a 520 4
1441.2.o \(\chi_{1441}(261, \cdot)\) n/a 520 4
1441.2.p \(\chi_{1441}(73, \cdot)\) n/a 520 4
1441.2.q \(\chi_{1441}(173, \cdot)\) n/a 520 4
1441.2.bb \(\chi_{1441}(304, \cdot)\) n/a 520 4
1441.2.bc \(\chi_{1441}(45, \cdot)\) n/a 1320 12
1441.2.bd \(\chi_{1441}(32, \cdot)\) n/a 1560 12
1441.2.bg \(\chi_{1441}(36, \cdot)\) n/a 6240 48
1441.2.bh \(\chi_{1441}(20, \cdot)\) n/a 6240 48
1441.2.bi \(\chi_{1441}(4, \cdot)\) n/a 6240 48
1441.2.bj \(\chi_{1441}(3, \cdot)\) n/a 6240 48
1441.2.bk \(\chi_{1441}(60, \cdot)\) n/a 6240 48
1441.2.bl \(\chi_{1441}(12, \cdot)\) n/a 5280 48
1441.2.bm \(\chi_{1441}(6, \cdot)\) n/a 6240 48
1441.2.bx \(\chi_{1441}(29, \cdot)\) n/a 6240 48
1441.2.by \(\chi_{1441}(2, \cdot)\) n/a 6240 48
1441.2.bz \(\chi_{1441}(18, \cdot)\) n/a 6240 48
1441.2.ca \(\chi_{1441}(10, \cdot)\) n/a 6240 48
1441.2.cb \(\chi_{1441}(83, \cdot)\) n/a 6240 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1441))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1441)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(131))\)\(^{\oplus 2}\)